Comparison load models in harmonic flows

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16 th International Conference and Exhibition on Electricity Distribution

CIRED 2001 - Session 2 : POWER QUALITY & EMC – Paper P2.43. RAI-Amsterdam. The Netherlands. 18-21 June 2001

COMPARISON LOAD MODELS IN HARMONIC FLOWS

V.F. Corasaniti, R. Bianchi, F. Viollaz

IITREE-LAT, Argentina

Abstract: With the increase of nonlinear loads in the distribution systems, it is important to carry out studies of harmonic flows with adequate models and to establish the possible resonances which can appear. This work has the aim to analize the influence of load model in the simulations, so that simulations with the load model CIGRE will be performed in contrast to the conventional model.

Keywords: Harmonics-Models-Simulation-Distortion

I.-INTRODUCTION

For the last years an important increase of nonlinear loads in the distribution systems has been produced. It has caused the increase of waveform voltage and current supply distortions with the consequent loss in the power quality. Also damage of the components of the networks has been produced such as in user’s equipment.

With the aim to study the distortion in the network studies of harmonic flows with apropiate models for that, these simulations will be carried out with the Electromagnetics Transients program ATP (Alternative Transients Program).

In this case, it will be made a study over a network of AT/MT (High voltage/ Medium voltage) (132/13.2kV), as, it is shown in Figure 1, which has installed capacitor banks in different substations.

The purpose of this study is to get the impedance versus frequency in different system points with both load models, using the capacity of ATP to make frequency scan.

FIGURE1- System to analize

Then it will be studied the distortions which appear due to the presence of harmonic sources in the network, using other capacities of program, (HFS, Harmonic Frequency Scan), which allow to introduce harmonics through current sources of amplitude, frecuency and phase established by the user.

II.-DEVELOPMENT

Figure 2 shows the scheme of the network made with the ATPDRAW, a draw pre-proccesor for the ATP.

TR1 TR2

CAP2

TR3

CAP3 LOAD3 LOAD2

LOAD1 SYSTEM

FIGURE2- Scheme of the network at ATP

The supply system of the network is represented with an equivalent at 132 kV through short-circuit reactance at that point, connected there to three other substations under study through underground cables at 132 kV. The loads connected in bus of 13.2 kV of each substation are from different values and each one has different degrees of reactive compensation.

Then it is carried out a description of adopted models and of data of each of the components used in the simulations.

II.1) Underground cables:

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TABLE1- Parámeters of cables

Cable SYST-TR1 TR1-TR2 TR2-TR3 Rated

Voltage [kV] 132 132 132 r [Ω/km] 0.052 0.059 0.063

r0 [Ω/km] 0.58 0.592 0.597

L [mH/km] 0.36 0.386 0.37

L0 [mH/km] 0.573 0.608 0.627

C [µF/km] 0.391 0.37 0.36

c0 [µF/km] 0.391 0.37 0.36

Length. [km] 2.4 1.82 2.75

II.2) Transformers:

It was not taken into account the parameter variations of transformers with the frequency. It was used a conventional model which does not have variation of resistence of winding with frequency.

Table 2 shows their characteristics.

TABLE2- Parámeters of transformers

TR

Rated Power [MVA]

Primary Voltage

[kV]

Secondary Voltage

[kV]

Connection X

[%]

TR1 20 132 13.2 13.02

TR2 40 132 13.2 12.45

TR3 80 132 13.2 27

II.3) Loads:

As it was said, the purpose of this work is to compare the results of simulations with two load models.

One of them does not have impedance variation of load with the frequency, (conventional model), while the other is a suggested model by CIGRE (1) for this kind of studies, which has variations of impedance load with the frequency.

Figure 3 shows the conventional single phase model.

FIGURE3- Modelo convencional

Figure 4 shows the single-phase model suggested by CIGRE.

The values of power demands in each subtation are shown in Table3.

FIGURE4- CIGRE model

TABLE3- Power demands

TR Pn

[MW]

Qn

[MVAr] Sn

[MVA]

TR1 13 6.5 14.5

TR2 13 6.5 14.5

TR3 26 10.86 28.2

II.4) Reactors and capacitors:

These were modelled like concentrated parameters, without taking into account any variation of inductance or capacitance with frecuency.

The values of reactive capacitor banks installed for power factor compensation in each subtation are shown in Table4.

TABLE4- Capacitors data

TR

Rated Voltage [kV]

Rated Current

[A]

Nº Q [MVAr]

TR2 13.2 210 1 4.8

TR3 13.2 210 2 9.6

Moreover, these capacitors have reactors in serie to limit inrush currents of their own. In Table5 these characterístics are detailed.

TABLE5- Reactors data

TR Un

[kV] In

[A] R [Ω]

L [mH]

TR2 15 210 0.0018 0.018

TR3 15 210 0.0018 0.018

III.-ANALYSIS

First we analyzed the frequency response in the following network points:

1. Equivalent connection system point in 132kV, Zs(w).

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Then, harmonic sources were applied in the connection load points, above mentioned. These sources were modelled with current sources with a characteristic spectrum of some nonlinear load, defined by harmonic order, amplitude and phase.

The distotions obtained at network points of interest will be analyzed and the differences between the results with both load models will be established.

IV.-SIMULATIONS

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IV.1)Simulations with FS (Frequency Scan)

Figure 5 shows the points where the frequency response of the network with both load models were obtained.

Zs(w)

Z1(w)

Z2(w)

Z3(w)

FIGURE5- Simulation de Z(w)

In Figure 6 it is shown the graph of Zs(w). In

Figures 7, 8 and 9, it is shown the graphs de Z1(w),

Z2(w) and Z3(w) also with both load models,

respectively.

It can be seen the differences between both models like in the amplification of the values and in the resonance frequency in these Figures.

FIGURE6- Zs(w) with both models

FIGURE7- Z1(w) with both models

The expression -[1]- was used to calculate the resonance frequency for CIGRE model in a network point, associated with the following values:

c c r

Q S f

f = -[1]-

CIGRE Conventional

Conventional CIGRE

Conventional

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where

fr: resonance frequency.

f: nominal o main frequency system. Sc: shortcircuit power at system point. Qc: reactive power of capacitor banks at that point.

In the substation 1, it is shown an amplification for high frequencies as in the substation there are no capacitor banks. The resonance is produced with the rest of the system. On the other hand, in the substation 2 it is produced a resonance around 400 Hz. That can be verified replacing in -[1]- a value of Sc established for the impedance of

tranformer (see table2) and the value of Qc for

substation 2 (see table4), resulting in:

Hz

Hz ₄₀₈

50 =

≅

Mvar 4.8

MVA 320 fr

Carrying out the same analysis for the substation 3, it is verified:

Hz

Hz ₂₈₀

50 =

≅

Mvar 9.6

MVA 300 f_r

Once the different frequency responses at interest system points are obtained, we get to know the troubles associated with the appearance of some harmonics. This can result from the own system (132 kV) or from the loads in some substations (13.2 kV).

Then harmonic currents will be only applied at user’s connection points and the differences in the distortions obtained with both models will be analysed.

IV.2) Simulations with HFS (Harmonic Frequency Scan)

To define the spectrum and amplitudes of currents it was taken into account the installation of six -pulse controlled rectifier for each substation, with an active power of 10 MW. Through -[2]- the value of nominal current of rectifier can be calculated in order to establish the amplitudes of harmonic currents:

ϕ ϕ

cos U 3

P I

cos I U 3 P

l act 1

1 l act

⋅ ⋅ =

⋅ =

-[2]-

where

Pact: value of active power. Ul: line voltage system. I1: nominal line current

Cosϕ: power factor of the load.

The rectifier which establishes a current spectrum like it is shown in Table 6, was considered ideal, supplied by a balance voltage system and without considering the phase, (see (2)),.

TABLE6- Values of currents

Harmonic Source

Ih Amp. Amp.[A]

I1 I1 514.6

I5 I1 / 5 102.9

I7 I1 / 7 73.5

I11 I1 / 11 46.8

I13 I1 / 13 39.6

I17 I1 / 17 30.3

I19 I1 / 19 27.1

The values of voltage obtained for each frequency will be the result from the multiplication provided in the ecuation -[3]-, that is to say to multiply the amplitudes of currents for the value of impedance obtained in IV.1) for the same harmonic.

[Vh] = [Ih]x[Zh] h=1,...20 -[3]-

In Figures 10, 11 and 12 the results obtained from simulations are shown.

FIGURE10- Voltage at substation1

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The graphs show the distortions found for the voltages in all substations. The blue bars correspond to CIGRE load model and the brown bars correspond to conventional model.

FIGURE12- Voltage at substation3

To establish the differences in the results obtained from both models, the factors established in -[4]- y -[5]- which determine the distortion degree for voltage waveform are calculated.

100

1 × =

U U h (%)

u

HF -[4]-

where

HFu: Harmonic Factor voltage of order h. Uh: harmonic amplitude voltage factor of order h.

U1: nominal harmonic amplitude of voltage.

100 U

U (%)

THD

1 2 u

2 h

u = ×

∑

∞

= -[5]-

where

THDu: Total Harmonic Distortion voltage. Supposing the amplitude voltage to nominal frequency is 13.2 kV, the values of Tables 7, 8 and 9 are obtained.

It can be observed the diferences in the distortions obtained with both models in the results. The differences in THD are higher in two first cases due to the high differences obtained in Z1(w) y Z2(w)

with respect to Z3(w), (see IV.1).

TABLE7- Distortioning comparison

Substation 1

CIGRE Conventional CIGRE Conventional

h

Voltage (V) Voltage (V) HF(%) HF(%)

5 452 574 3,42 4,35

7 410 530 3,11 4,02

11 353 448 2,67 3,39

13 337 412 2,55 3,12

17 343 363 2,60 2,75

19 270 280 2,05 2,12

THD 6,78 8,27

Substation 2

h

5 424 526 3,21 3,98

7 697 886 5,28 6,71

11 365 251 2,77 1,90

13 188 148 1,42 1,12

17 71 64 0,54 0,48

19 70 65 0,53 0,49

THD 6,96 8,14

Substation 3

h

5 546 673 4,14 5,10

7 518 311 3,92 2,36

11 118 92 0,89 0,70

13 74 61 0,56 0,46

17 35 32 0,27 0,24

19 30 25 0,23 0,19

THD 5,81 5,69

V.- CONCLUSIONS

When studies or simulation of harmonics are carried out, it is important to use some load model which has parameter variation with frequency, such as the suggested CIGRE model, because there are evident differences between the distortions.

In the Regulations of our country, (see (3)), limits are established for each Harmonic Factor (HF) from 0.2% to 6% and also limits for Total Harmonic Distortion (THD) which is 8% for medium level voltage. Therefore the differences of 1.5% y 1.18% found between both models, (see Table 7 and 8 respectively), can result from overcoming those levels in the network.

V.- REFERENCIAS

1. CIGRE Working Group 36-05 (Disturbing Loads),1981, “Harmonics, characterisitic parameters, methods of study, estimates of existing values in the network”.

Electra, 77, 35-54.

2. J. Arrillaga, D. A. Bradley y P. S. Bodger (1985), Power System Harmonics.